How true is this “In this case, however, the convexity of the liabilities is less than the convexity of the assets. Therefore, the decline in value of the liabilities as a result of the yield curve shift will be greater than the decline in value of the assets, thus increasing economic surplus.”
sounds true to me
Why
Because more convexity means the value is decreasing at a decreasing rate when interest rates are falling.
Draw a graph with a linear line from the upper left side of the graph to the bottom right side. This is your duration measurement.
Now draw a concave curve that intersects duration near the middle of the graph.
Now draw a more concave curve that intersecpts duration at the same middle position in the graph
The more convcave curve is the curve with more convexity. If you look towards the right side you’ll see the more convex curve is worth more in comparision to the curve with less convexity (value being on the Y axis and interest on the X axis)